1. If the threshold is the membrane potential AT WHICH sufficient number of Na+-voltage gated channels OPEN such that the membrane permability of sodium is greater than potassium, then HOW (in general) does the membrane potential get to the threshold in the first place?

Attempt: a stimulus causes the activation of special ion channels (not the voltage-gated ones) that cause ions that go into the cell which induce depolarization (for instance: the Na+ ion influx). Given that the influx via these special channels reaches threshold, THEN the Na-VG channels open, and as a result, an AP is generated.

2. Why is it that axons with thin diameters need to have more ion channels, while those that are fatter (wider diameters) can have relatively fewer, and yet still sustain AP propagation down the axon?

Attempt: there is not enough space within a thinner axon to withhold the large, brief intake of positive charge?

I think the second question is referring to thicker axons having nodes of Ranvier and thus can perform saltatory conduction. This would decrease the need for Na+ channels. The answer to the first question sounds pretty reasonable.